2.3.35 Problems 3401 to 3500

Table 2.643: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3401	10795	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
3402	15080	\begin{align*} x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x&=t^{2}-3 \\ \end{align*}	✓	✓	✓	✓	0.279
3403	16801	\begin{align*} y^{\prime }&=3 \delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.279
3404	19688	\begin{align*} x^{\prime \prime }-5 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3405	20490	\begin{align*} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3406	21712	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.279
3407	26018	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
3408	27606	\begin{align*} y y^{\prime \prime }&=2 {y^{\prime }}^{2} x \\ y \left (2\right ) &= 2 \\ y^{\prime }\left (2\right ) &= {\frac {1}{2}} \\ \end{align*}	✗	✓	✓	✗	0.279
3409	27640	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=4 x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.279
3410	27661	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{x}+5 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.279
3411	1772	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.280
3412	3060	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3413	8629	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
3414	9386	\begin{align*} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.280
3415	10806	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3416	10953	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
3417	11166	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3418	11215	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3419	12778	\begin{align*} \sin \left (x \right )-\cos \left (x \right ) y-3 \sin \left (x \right ) y^{\prime }+3 \left (1+\cos \left (x \right )\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
3420	23675	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
3421	23699	\begin{align*} y^{\prime \prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
3422	27122	\(\left [\begin {array}{cc} 6 & 1 \\ 1 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.280
3423	440	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
3424	857	\begin{align*} y^{\prime \prime }-2 i y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3425	8624	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 28 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
3426	9022	\begin{align*} 2 y x +\left (x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3427	10746	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3428	10784	\begin{align*} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3429	11052	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3430	11220	\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3431	14998	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.281
3432	15972	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.281
3433	16670	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.281
3434	23055	\begin{align*} r^{\prime }&=-a \sin \left (\theta \right ) \\ r \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	0.281
3435	410	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
3436	439	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
3437	3950	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.282
3438	7825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.282
3439	8531	\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.282
3440	10103	\begin{align*} y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3441	10807	\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3442	10865	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3443	11017	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3444	11035	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3445	11060	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3446	12564	\begin{align*} \left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
3447	16784	\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.282
3448	22779	\begin{align*} y^{\prime \prime \prime }-4 y&=4 x +2+3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.282
3449	23313	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
3450	234	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
3451	1764	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=-6 x -4 \\ \end{align*}	✓	✓	✓	✓	0.283
3452	3199	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.283
3453	3928	\begin{align*} y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
3454	7450	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
3455	7832	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
3456	7853	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
3457	8623	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
3458	9107	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.283
3459	10732	\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
3460	11201	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
3461	13138	\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.283
3462	16727	\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
3463	18966	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✗	0.283
3464	19593	\begin{align*} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.283
3465	27765	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.283
3466	1061	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.284
3467	4490	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.284
3468	7044	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
3469	10947	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
3470	11064	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
3471	15705	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.284
3472	16514	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
3473	16767	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.284
3474	16792	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.284
3475	17017	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
3476	26444	\begin{align*} y^{\prime \prime \prime }&=\frac {x}{\left (x +2\right )^{5}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.284
3477	3572	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
3478	4370	\begin{align*} y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.285
3479	7907	\begin{align*} -y-{\mathrm e}^{x} x^{2}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
3480	10632	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3481	10637	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3482	11026	\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3483	11057	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3484	12297	\begin{align*} y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3485	14340	\begin{align*} x^{\prime \prime }-x^{\prime } t +x&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3486	15297	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
3487	16035	\begin{align*} y^{\prime \prime }-6 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
3488	16966	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
3489	1071	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
3490	1273	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
3491	1396	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
3492	1742	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
3493	2204	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.286
3494	3685	\begin{align*} y+3 x^{2}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
3495	10355	\begin{align*} y^{\prime }+\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.286
3496	10742	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.286
3497	11074	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
3498	13174	\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.286
3499	16712	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
3500	20124	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.286